# ---
# title: 37. Sudoku Solver
# id: problem37
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Hash Table, Backtracking
# link: <https://leetcode.com/problems/sudoku-solver/description/>
# hidden: true
# ---
# 
# Write a program to solve a Sudoku puzzle by filling the empty cells.
# 
# A sudoku solution must satisfy **all of  the following rules**:
# 
#   1. Each of the digits `1-9` must occur exactly once in each row.
#   2. Each of the digits `1-9` must occur exactly once in each column.
#   3. Each of the digits `1-9` must occur exactly once in each of the 9 `3x3` sub-boxes of the grid.
# 
# The `'.'` character indicates empty cells.
# 
# 
# 
# **Example 1:**
# 
# ![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-
# by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png)
# 
#     
#     
#     Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
#     Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
#     Explanation:  The input board is shown above and the only valid solution is shown below:
#     
#     ![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png)
#     
# 
# 
# 
# **Constraints:**
# 
#   * `board.length == 9`
#   * `board[i].length == 9`
#   * `board[i][j]` is a digit or `'.'`.
#   * It is **guaranteed** that the input board has only one solution.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
